Analysis of a post-fracture pressure buildup test with wellbore-storage distortion

Input(s)

$$q_{g}$$: Gas flow rate (MSCF/day)

$$B_{g}$$: Gas formation Volume Factor (RB/MSCF)

$$p_{D}$$: Dimensionless Pressure (dimensionless)

$$\varnothing$$: Porosity (dimensionless)

$$c_{t}$$: Compressibility $$(1 / \mathrm{psi})$$

$$\mu$$: Viscosity $$(\mathrm{cP})$$

$$\mathrm{h}$$: Formation Thickness (ft)

$$t_{\left(L_{\rangle_{D}}\right.}$$: Time of end of linear or pseudo radial flow from plot (dimensionless)

$$C_{r D}$$: Dimensionless fracture conductivity (dimensionless)

$$C_{f D}$$: Dimensionless Wellbore storage coefficient (dimensionless)

$$L_{f}$$: Length of fracture $$(\mathrm{ft})$$

$$\mathrm{k}$$: Permeability $$(\mathrm{mD})$$

$$\Delta t_{A E}$$: Equivalent Adjusted delta time from derivative curve (h)

Output(s)

C: Well bore storage coefficient (bbl/psi)

$$w_{f k_{f}}$$: Min Fracture conductivity for infinite conductive fracture $$(\mathrm{mD} \mathrm{ft})$$

$$L_{f M P}$$: Length of fracture from match point analysis (ft)

$$\left(\Delta P_{a}\right)_{M P}$$: Adjusted Pressure difference at match point from plot (psi)

Formula(s)

$\begin{gathered} C=\left(141.2 * q_{g} * B_{g} * \frac{\mu}{k * h}\right) *\left(p_{D}\right)_{M P} \\ w_{f k_{f}}=\left(\left(\frac{0.0002637 * k}{\varnothing * \mu * c_{t}}\right) *\left(\frac{\Delta t_{A E}}{t_{\left(L_{f}\right)_{D}}}\right)_{M P}\right)^{\frac{1}{2}} \\ L_{f M P}=\left(\emptyset * h * c_{t} * \frac{L_{f}^{2}}{0.8936}\right) * C_{f D} \\ \left(\Delta P_{a}\right)_{M P}=3.14 * k * C_{r D} * L_{f} \end{gathered}$

Reference(s)

Lee, J., Rollins J.B., and Spivey J.P. 2003, Pressure Transient Testing, Vol. 9, SPE Textbook Series, Vol. 9 , Henry L. Doherty Memorial Fund of AIME, Richardson, Texas, SPE, Chapter: 6, Page: 127.

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Analysis of a post-fracture - Constant-rate flow test with boundary effects

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